284 Formation of Compound or_ Twin Crystals. 



latter was the case, the secondary planes would not be symmetric- 

 ally arranged relatively to these axes. According to the liypothesis 

 of three axes, the planes on the terminal edges are tangents to the 

 point of equilibrium between two poles at the same extremity of the 

 ellipsoid, as (Fig. 7,) between N''' and JV', (the italic letters are 

 here used instead of the dotted posterior ones in the figures,) N' and 

 N'', and N'^ and N'^', and also the same at the other extremity ; 

 those on the lateral edges, to similar points between a pole at each 

 extremity, or between S' and N'^ S' and N'", *S'" and N^'', S" and 

 N', &c. The plane truncating the terminal solid angles touches 

 the point of equilibrium between the three poles N", JV, N'"', or S', 

 ♦S'''', S'^' ; those on the lateral angles, (prismatic planes,) similar 

 points between one pole at one extremity of the ellipsoid, and two 

 at the other as between S', N"^, N'', he. The same law is through- 

 out followed, as in the construction of the secondaries of the Cube 

 and the Prisms, which could not be the fact with any other diposi- 

 tion of the axes. 



The hemihedral modifications, that is, those in which but half the 

 number of secondary planes occur, which perfect obedience to law 

 would require, are exceptions to the general principle laid down, 

 that all similarly situated points in a molecule are opposed to simi- 

 lar planes. The Cubes of Pyrites, modified with the planes of the 

 Pentagonal Dodecahedron are instances. Also those crystals of 

 Quartz in which every other pair only of the lateral solid angles of 

 the prisms are replaced by a plane. These planes are the result of 

 a bevelraent of only the alternate lateral edges, or those inclined in 

 the same direction, for instance the edges a in Fig. 7, or at other 

 times the edges b. The attraction in each pole at one extremity of 

 the ellipsoid appears to have been modified only in its relation to 

 one at the other extremity instead of two, from which it is equally 

 distant. Some peculiar kind of influence, probably electrical, seems 

 to have been exerted between the poles at one end and those to the 

 right or those to the left at the other. There is an undoubted con- 

 nection between the cause and that of the peculiarly interesting op- 

 tical phenomenon observed by Mr. Herschel in similar crystals hav- 

 ing oblique faces on each of the solid angles ; 1 refer to their turning 

 the planes of polarization to the right or left according to the inclina- 

 tions of these faces to the right or left hand. A complete knowl- 

 edge of the facts that electricity may hereafter develop, will prob- 

 ably elucidate fully this point. These irregularities do not militate 



